Home
Class 12
MATHS
If (2x^2+3x+4)^(10)=sum(r=0)^(20) ar x^r...

If `(2x^2+3x+4)^(10)=sum_(r=0)^(20) a_r x^r`, then `(a_7)/(a_(13)`=

A

`6`

B

`8`

C

`12`

D

`16`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` Given `(2x^(2)+3x=4)^(10)=sum_(r=0)^(20)a_(r )x^(r )`
Replacing `x` by `(2)/(x)`, we get
`((8)/(x^(2))+(6)/(x)+4)^(10)=sum_(r=0)^(20)a_(r )((2)/(x))^(r )`
`implies2^(10)(2x^(2)+3x+4)^(10)=sum_(r=0)^(20)a_(r )2^(r )x^(20-r)`
`impliessum_(r=0)^(20)a_(r )x^(r )=sum_(r=0)^(20)a_(r )2^(r-10)x^(20-r)`
Comparing coefficient `x^(7)` both sides , we get `a_(7)=a_(13)xx2^(3)`.
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE|Exercise Multiple Correct Answer|4 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise Comprehension|11 Videos

  • BINOMIAL THEOREM

    CENGAGE|Exercise JEE Previous Year|16 Videos

  • AREA UNDER CURVES

    CENGAGE|Exercise Question Bank|20 Videos

  • BINOMIAL THEORM

    CENGAGE|Exercise Question Bank|31 Videos

Similar Questions

Explore conceptually related problems

If (1-x-x^(2))^(20)=sum_(r=0)^(40)a_(r).x^(r), then

If (1-x-x^(2))^(20)=sum_(r=0)^(40)a_(r)x^(r), then a_(1)+3a_(3)+5a_(5)+.......+39a_(39)=

If (1+x-2x^(2))^(6)=sum_(r=0)^(12)a_(r).x^(r) then a_(1)+a_(3)+......a_(11)

If (1+x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then a_(1)-2a_(2)+3a_(3)-...-2na_(2n)=

(1+x-2x^(2))^(6)=sum_(r=0)^(12)a_(r)x^(r) then a_(2)+a_(4)+....+a_(12)=

If (1+x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then prove that a_(r)=a_(2n-r)

If (1+2x+x^(2))^(n)=sum_(r=0)^(2n)a_(r)x^(r), then a=(^(n)C_(2))^(2) b.^(n)C_(r).^(n)C_(r+1) c.^(2n)C_(r) d.^(2n)C_(r+1)

if (1-x+2x^(2))^(10)=sum_(0)^(20)a_(r)*x^(r) then find sum_(1)^(10)a_(2r-1)

CENGAGE-BINOMIAL THEOREM-Single correct Answer
  1. The sum S(n)=sum(k=0)^(n)(-1)^(k)*^(3n)C(k), where n=1,2,…. is

    Text Solution

    |

  2. If for n in I , n > 10 ;1+(1+x)+(1+x)^2++(1+x)^n=sum(k=0)^n ak*x^k ...

    Text Solution

    |

  3. Given "^(8)C(1)x(1-x)^(7)+2*^(8)C(2)x^(2)(1-x)^(6)+3*^(8)C(3)x^(3)(1-x...

    Text Solution

    |

  4. The value of 99^(50)-(99)/(1)*98^(50)+(99.98)/(1.2)97^(50)-……-(99.98)/...

    Text Solution

    |

  5. Let f(n)= (k=1)Σ^n k^2(n Ck)^ 2 then the value of f(5) equals

    Text Solution

    |

  6. The value of sum(r=1)^(n)(-1)^(r-1)((r )/(r+1))*^(n)C(r ) is

    Text Solution

    |

  7. The value of ((100),(0))((200),(150))+((100),(1))((200),(151))+......+...

    Text Solution

    |

  8. Let t(100)=sum(r=0)^(100)(1)/(("^(100)C(r ))^(5)) and S(100)=sum(r=0)^...

    Text Solution

    |

  9. Let S(1)=underset(0 le i lt j le 100)(sumsum)C(i)C(j), S(2)=underset(0...

    Text Solution

    |

  10. "^(74)C(37)-2 is divisibl by

    Text Solution

    |

  11. If "^(n)C(0)-^(n)C(1)+^(n)C(2)-^(n)C(3)+...+(-1)^(r )*^(n)C(r )=28 , t...

    Text Solution

    |

  12. If the value of "^(n)C(0)+2*^(n)C(1)+3*^(n)C(2)+...+(n+1)*^(n)C(n)=576...

    Text Solution

    |

  13. The value of ((50),(6))-((5),(1))((40),(6))+((5)/(2))((30),(6))-((5),(...

    Text Solution

    |

  14. The value of the expansion (sumsum)(0 le i lt j le n) (-1)^(i+j-1)"^(n...

    Text Solution

    |

  15. sum(m=1)^(n)(sum(k=1)^(m)(sum(p=k)^(m)"^(n)C(m)*^(m)C(p)*^(p)C(k)))=

    Text Solution

    |

  16. If ((1-3x)^(1//2)+(1-x)^(5//3))/(sqrt(4-x)) is approximately equal to ...

    Text Solution

    |

  17. The sum of the series 1 + (1)/(3^(2)) + (1 *4)/(1*2) (1)/(3^(4))+( ...

    Text Solution

    |

  18. Coefficient of x^(2^(m+1)) in the expansion of 1/((1+x)(1+x^2)(1+x^4)(...

    Text Solution

    |

  19. If (2x^2+3x+4)^(10)=sum(r=0)^(20) ar x^r, then (a7)/(a(13)=

    Text Solution

    |

  20. "^(30)C(0)*^(20)C(10)+^(31)C(1)*^(19)C(10)+^(32)C(2)*18C(10)+....^(40)...

    Text Solution

    |